We introduce EL PASSO, a privacy-preserving, asynchronous Single Sign-On (SSO) system. It enables personal authentication while protecting users' privacy against both identity providers and relying parties, and allows selective attribute disclosure. EL PASSO is based on anonymous credentials, yet it supports users' accountability. Selected authorities may recover the identity of allegedly misbehaving users, and users can prove properties about their identity without revealing it in the clear. EL PASSO does not require specific secure hardware or a third party (other than existing participants in SSO). The generation and use of authentication credentials are asynchronous, allowing users to sign on when identity providers are temporarily unavailable. We evaluate EL PASSO in a distributed environment and prove its low computational cost, yielding faster sign-on operations than OIDC from a regular laptop, one-second user-perceived latency from a low-power device, and scaling to more than 50 sign-on operations per second at a relying party using a single 4-core server in the cloud.